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Parameter estimation from Rician‐distributed data sets using a maximum likelihood estimator: Application to t 1 and perfusion measurements
Author(s) -
Karlsen Ole T.,
Verhagen Rieko,
Bovée Wim M.M.J.
Publication year - 1999
Publication title -
magnetic resonance in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.696
H-Index - 225
eISSN - 1522-2594
pISSN - 0740-3194
DOI - 10.1002/(sici)1522-2594(199903)41:3<614::aid-mrm26>3.0.co;2-1
Subject(s) - estimator , maximum likelihood , estimation theory , computer science , rician fading , estimation , statistics , mathematics , algorithm , decoding methods , fading , management , economics
Abstract General expressions are presented to calculate the maximum likelihood (ML) estimator and corresponding Fisher matrix for Rician‐distributed data sets. This estimator results in the most precise, unbiased estimations of T 1 from magnitude data sets, even when low signal‐to‐noise ratios (<6) are present. By optimizing the sample point distributions for inversion‐recovery experiments, a 32% increase in precision of the estimated T 1 is obtained, compared with a linear sampling scheme. Perfusion rates are estimated from combined data sets of the slice‐ and nonslice‐selective inversion‐recovery experiments, as obtained with the flow‐sensitive alternating inversion recovery (FAIR) technique. The ML estimator for the combined data set results in the most precise, unbiased estimations of the perfusion rate. Error analysis shows that very high signal‐to‐noise ratios are required for precise estimation of perfusion rates from FAIR experiments. Magn Reson Med 41:614–623, 1999. © 1999 Wiley‐Liss, Inc.